Q1: Heat flow across a hollow sphere of inner radius 'r₁' and outer radius 'r₂' is directly proportional to

ANS:B -

The heat flow across a hollow sphere of inner radius r1​ and outer radius r2​ is directly proportional to several factors:

1. Temperature Difference (ΔT): The rate of heat flow (heat transfer per unit time) is directly proportional to the temperature difference across the sphere. According to Fourier's Law of Heat Conduction, the rate of heat transfer (Q) is given by Q=kA(ΔT/d)​, where k is the thermal conductivity, A is the cross-sectional area, and d is the thickness of the material through which heat flows.
2. Thermal Conductivity (k): The rate of heat flow is also directly proportional to the thermal conductivity of the material of the sphere. Materials with higher thermal conductivity allow heat to flow more easily through them.
3. Surface Area (A): The rate of heat flow is proportional to the surface area of the sphere. A larger surface area allows more heat to transfer across the surface.
4. Inverse of Thickness (d1​): The rate of heat flow is inversely proportional to the thickness of the material through which heat flows. Thicker materials offer more resistance to heat flow.
5. Geometry of the Sphere: The geometry of the sphere, particularly the thickness of the shell, affects the rate of heat flow. Thicker shells provide more resistance to heat flow compared to thinner shells.

Therefore, the rate of heat flow across a hollow sphere of inner radius r1​ and outer radius r2​ is directly proportional to the temperature difference across the sphere, the thermal conductivity of the material, the surface area, and inversely proportional to the thickness of the shell.